Digital data communication over a wireless channel is used in a variety of applications. One way to encode digital information in an RF signal is by manipulating the phase and/or magnitude of the signal in dependence on the digital information which is to be transmitted. At the receiving end the magnitude and/or phase changes are detected and the digital information is reconstructed. Transmitting data by encoding the information in phase is referred to as phase-shift keying (PSK). For example, it conveys data by modulating the phase of a reference signal (the carrier wave).
Phase-shift keying (PSK) is used in a variety of applications such as: communication to and from RFID tags, wireless LAN, including Wi-Fi, DAB, DAB+, and Bluetooth. PSK may use a finite number of phases to represent digital data, also called symbols. Each phase may be assigned a unique pattern of binary digits.
At the transmitter side, a modulator maps digital information to a sequence of symbols which in turn is encoded in the phase changes of a signal which is to be transmitted using an antenna. At the receiver end, a demodulator determines the phase of the received signal and maps it back to the symbol it represents, thus recovering the original digital information. Typically, the demodulator is designed specifically for the symbol-set used by the modulator.
The wireless channel interacts with the transmitted signal through the so called channel frequency response. The received signal equals the transmitted signal multiplied with the channel frequency response plus additive white Gaussian noise, that is: yl=Hlsl+nl. In this formula: yl represents the l'th received signal, Hl the frequency response, sl the transmitted symbol, and nl the noise. Note that the entities are modeled as complex numbers, either representing a combination of an In-phase and quadrature component, or as a combination of magnitude and phase. One representation may be converted into the other as convenient.
To complicated matters further, the channel frequency response is not constant, in particular if the receiver is mobile, e.g., a car, the channel frequency response will change considerably with time.
Two principal solutions have been proposed to the problem that the transmitted symbols have been multiplied with an unknown channel frequency response before they received signals.
First: In so-called coherent reception schemes coherently modulated symbols are used with pre-determined training sequences or ‘pilots’ in the transmitted signal. Coherent demodulation requires channel state information which can be obtained by comparing the received pilots with knowledge about the pilots as they are transmitted.
Second: Differential modulation is a special modulation technique which can be demodulated with a non-coherent receiver, i.e., a conventional differential demodulator can demodulate the symbols without using any channel estimation or equalization processes at the receiver simplifying the receiver structure. Due to this property, differential modulation has been chosen as the modulation scheme in several wireless standards, e.g., DAB, T-DMB etc.
Although differential modulation allows simpler receivers, the method is not without its problems: The first drawback of differential modulation and demodulation is that it assumes the channel remains almost static during the two symbols where differential modulation is used. However, this assumption does not hold true in mobile reception where differential modulation is applied in time direction, e.g., over successive OFDM symbols in DAB family of standards or frequency selective reception where differential modulation is applied in frequency direction, e.g., over successive subcarriers of an OFDM symbol. As a result of this, the performance degrades with increased mobility and/or frequency selectivity.
Another drawback of differential demodulation is due to the encoding of the data in two successive symbols. This causes two noise sources affecting the demodulation process even if the channel is static, leading to approximately 3 dB performance loss.